All of these currently serve as websites on one of my computers, located internally at 192.168.1.3. This is accomplished because port 80 forwards to this internal computer.

However, I want subdomain4.domain4.com to now point a different computer, located at 192.168.1.5. The reason is because this website uses a lot of resources and I want it to be located on its own computer.

Is this possibe with my router. I have the official Linksys firmware, which is version 4.30.5. I am willing to flash a new firmware to accomplish this. Thanks!

Sorry, SOHO (Small Office, Home Office) routers/firewalls such as the Linksys only handel 1 external IP address, and therfore can only port forward the HTTP port 80 to one inside address.

Your option would be to host the second site on an alternate port, perhaps 8080, but this is not a great idea.

What you really want is to ask your ISP if you can have multiple static IP addresses, and then get a router/firewall like the Cisco PIX 501/506/515 series of devices - which will handle multiple IPs and multiple port 80 port forward rules